This paper offers an extensive review of publications dealing with the modeling, the design, and the experimental investigation of grooved dynamic gas-lubricated bearings. Recent years have witnessed a rise in small-scale and high-speed turbomachinery applications. Besides the well-known gas foil bearings, grooved bearings offer attractive advantages, which unveil their potential in particular at small scale due to the structural simplicity as well as satisfying predictability. This paper starts with a general background of the application of gas-lubricated bearings and introduces and compares the different gas bearing topologies. Further, the state-of-the-art modeling of grooved gas-lubricated bearings is introduced, systematically assessing the advantages and inconveniences of two major approaches, i.e., the narrow groove theory (NGT) and direct discretization method. Since the NGT method is an elegant and efficient approach to model the complex effects of periodic grooves, a critical section is dedicated to the NGT. In a second phase, different models to include additional physical phenomena such as real gas lubrication, rarefaction, or turbulence effects are reviewed. The paper concludes with a critical assessment of the state-of-the-art and indicates potential fields of research that would allow to shed more light into the understanding of these bearings, as well as with some thoughts on the integrated design methodologies of gas bearing supported rotors.

Multi-objective optimization is increasingly used in engineering to design new systems and to identify design trade-offs. Yet, design problems often have objective functions and constraints that are expensive and highly non-linear. Combinations of these features lead to poor convergence and diversity loss with common algorithms that have not been specifically designed for constrained optimization. Constrained benchmark problems exist, but they do not necessarily represent the challenges of engineering problems. In this paper, a framework to design electro-mechanical actuators, called MODAct, is presented and 20 constrained multi-objective optimization test problems are derived from the framework with a specific focus on constraints. The full source code is made available to ease its use. The effects of the constraints are analyzed through their impact on the Pareto front as well as on the convergence performance. A constraint landscape analysis approach is followed and extended with three new metrics to characterize the search and objective spaces. The features of MODAct are compared to existing test suites to highlight the differences. In addition, a convergence analysis using NSGA-II, NSGA-III and C-TAEA on MODAct and existing test suites suggests that the design problems are indeed difficult due to the constraints. In particular, the number of simultaneously violated constraints in newly generated solutions seems key in understanding the convergence challenges. Thus, MODAct offers an efficient framework to analyze and handle constraints in future optimization algorithm design.

Experimental evidence in the literature suggests that foil bearing-supported rotors can suffer from subsynchronous vibration. While dry friction between top foil and bump foil is thought to provide structural damping, subsynchronous vibration is still an unresolved issue. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing-supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear, rotordynamic model. A sensitivity analysis suggests that structural damping has limited effect on stability. Further, it is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore, selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multiobjective optimization using the foil bearing-supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that, with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2), the optimum shim patterns vary little with bearing geometry; thus, a generalized shim pattern is proposed for low compressibility numbers.

Domestic heating and cooling will more and more have to rely on heat pumps (HPs) in order to support a more rational use of primary energy consumption. The HP market is mainly dominated by electrically driven vapor compression cycles and by thermally driven sorption processes. The drawback of electrically driven vapor compression cycle is their dependence on an electrical grid and the fact that they increase the winter or summer electricity peak demands. Hence, a thermally driven vapor compression cycle would offer substantial advantages and flexibility to the end user for heating and cooling applications. This paper presents the investigation of an oil-free compressor-turbine unit (CTU) used for a thermally driven HP (TDHP) based on the combination of a HP compression cycle and an organic Rankine cycle (ORC). The CTU consists of a radial inflow turbine and a centrifugal compressor of the order of 2 kW each, directly coupled through a shaft supported on gas lubricated bearings. The CTU has been tested at rotor speeds in excess of 200 krpm, reaching compressor and turbine pressure ratios up to 2.8 and 4.4, respectively, and isentropic efficiencies around 70%. Comparisons between the experimental data and predictions of models, that are briefly described here, have been carried out. A sensitivity analysis based on the experimentally validated models shows that tip clearance, for both compressor and turbine, and surface roughness of the compressor are key parameters for further improving performance.

Although gas-lubricated herringbone grooved journal bearings (HGJB) are known for high rotordynamic stability thresholds, small clearance to diameter ratios are required for stable rotor operation. Tight clearances not only increase bearing losses but also yield challenging manufacturing and assembly tolerances, which ultimately translate into cost. Traditionally, the grooves of HGJB are of helical nature with constant cross section and pitch. The current paper aims at increasing the clearance to diameter ratio and the stability threshold of grooved bearings by introducing enhanced groove geometries. The axial evolution of groove width, depth, and local pitch are described by individual third order polynomials with four interpolation points. The expression for the smooth pressure distribution resulting from the narrow groove theory is modified to enable the calculation of bearing properties with modified groove patterns. The reduced order bearing model is coupled to a linear rigid body rotordynamic model for predicting the whirl speed map and the corresponding stability. By introducing a critical mass parameter as a measure for stability, a criterion for the instability onset is proposed. The optimum groove geometry is found by coupling the gas bearing supported rotor model with a multiobjective optimizer. By maximizing both the clearance to diameter ratio and the rotordynamic stability it is shown that with optimal groove geometry, which deviates from helicoids with constant pitch and cross section, the critical mass parameter can be improved by more than one order of magnitude compared to traditional HGJB geometries. The clearance to diameter ratio can be increased by up to 80% while keeping the same stability margin, thus reducing both losses and manufacturing constraints. The optimum groove pattern distributions (width ratio, angle, and depth) are summarized for a variety of L/D ratios and for different compressibility numbers in a first attempt to set up general design guidelines for enhanced gas-lubricated HGJB.